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      1 /*
      2 Copyright (c) 2014, Intel Corporation
      3 All rights reserved.
      4 
      5 Redistribution and use in source and binary forms, with or without
      6 modification, are permitted provided that the following conditions are met:
      7 
      8     * Redistributions of source code must retain the above copyright notice,
      9     * this list of conditions and the following disclaimer.
     10 
     11     * Redistributions in binary form must reproduce the above copyright notice,
     12     * this list of conditions and the following disclaimer in the documentation
     13     * and/or other materials provided with the distribution.
     14 
     15     * Neither the name of Intel Corporation nor the names of its contributors
     16     * may be used to endorse or promote products derived from this software
     17     * without specific prior written permission.
     18 
     19 THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS IS" AND
     20 ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED
     21 WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE
     22 DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT OWNER OR CONTRIBUTORS BE LIABLE FOR
     23 ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES
     24 (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES;
     25 LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON
     26 ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT
     27 (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS
     28 SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
     29 */
     30 
     31 /******************************************************************************/
     32 //                     ALGORITHM DESCRIPTION
     33 //                     ---------------------
     34 //
     35 //    Let x=2^k * mx, mx in [1,2)
     36 //
     37 //    Get B~1/mx based on the output of rcpss instruction (B0)
     38 //    B = int((B0*LH*2^7+0.5))/2^7
     39 //    LH is a short approximation for log10(e)
     40 //
     41 //    Reduced argument: r=B*mx-LH (computed accurately in high and low parts)
     42 //
     43 //    Result:  k*log10(2) - log(B) + p(r)
     44 //             p(r) is a degree 7 polynomial
     45 //             -log(B) read from data table (high, low parts)
     46 //             Result is formed from high and low parts
     47 //
     48 // Special cases:
     49 //  log10(0) = -INF with divide-by-zero exception raised
     50 //  log10(1) = +0
     51 //  log10(x) = NaN with invalid exception raised if x < -0, including -INF
     52 //  log10(+INF) = +INF
     53 //
     54 /******************************************************************************/
     55 
     56 #include <private/bionic_asm.h>
     57 # -- Begin  static_func
     58         .text
     59         .align __bionic_asm_align
     60         .type static_func, @function
     61 static_func:
     62 ..B1.1:
     63         call      ..L2
     64 ..L2:
     65         popl      %eax
     66         lea       _GLOBAL_OFFSET_TABLE_+[. - ..L2](%eax), %eax
     67         lea       static_const_table@GOTOFF(%eax), %eax
     68         ret
     69         .size   static_func,.-static_func
     70 # -- End  static_func
     71 
     72 # -- Begin  log10
     73 ENTRY(log10)
     74 # parameter 1: 8 + %ebp
     75 ..B2.1:
     76 ..B2.2:
     77         pushl     %ebp
     78         movl      %esp, %ebp
     79         subl      $104, %esp
     80         movl      %ebx, 40(%esp)
     81         call      static_func
     82         movl      %eax, %ebx
     83         xorpd     %xmm2, %xmm2
     84         movl      $16368, %eax
     85         pinsrw    $3, %eax, %xmm2
     86         movl      $1054736384, %ecx
     87         movd      %ecx, %xmm7
     88         xorpd     %xmm3, %xmm3
     89         movl      $30704, %edx
     90         pinsrw    $3, %edx, %xmm3
     91         movsd     112(%esp), %xmm0
     92         movapd    %xmm0, %xmm1
     93         movl      $32768, %edx
     94         movd      %edx, %xmm4
     95         movapd    2128(%ebx), %xmm5
     96         pextrw    $3, %xmm0, %eax
     97         orpd      %xmm2, %xmm0
     98         movl      $16352, %ecx
     99         psllq     $5, %xmm0
    100         movsd     2144(%ebx), %xmm2
    101         psrlq     $34, %xmm0
    102         rcpss     %xmm0, %xmm0
    103         psllq     $12, %xmm1
    104         pshufd    $78, %xmm5, %xmm6
    105         psrlq     $12, %xmm1
    106         subl      $16, %eax
    107         cmpl      $32736, %eax
    108         jae       .L_2TAG_PACKET_0.0.2
    109 .L_2TAG_PACKET_1.0.2:
    110         mulss     %xmm7, %xmm0
    111         orpd      %xmm3, %xmm1
    112         andpd     %xmm1, %xmm5
    113         paddd     %xmm4, %xmm0
    114         subsd     %xmm5, %xmm1
    115         movd      %xmm0, %edx
    116         psllq     $29, %xmm0
    117         andpd     %xmm6, %xmm0
    118         andl      $32752, %eax
    119         subl      %ecx, %eax
    120         cvtsi2sdl %eax, %xmm7
    121         mulpd     %xmm0, %xmm5
    122         mulsd     %xmm0, %xmm1
    123         movsd     2064(%ebx), %xmm6
    124         movapd    2080(%ebx), %xmm3
    125         subsd     %xmm2, %xmm5
    126         andl      $16711680, %edx
    127         shrl      $12, %edx
    128         movapd    -1504(%ebx,%edx), %xmm0
    129         movapd    2096(%ebx), %xmm4
    130         addsd     %xmm5, %xmm1
    131         movapd    2112(%ebx), %xmm2
    132         mulsd     %xmm7, %xmm6
    133         pshufd    $68, %xmm1, %xmm5
    134         mulsd     2072(%ebx), %xmm7
    135         mulsd     %xmm1, %xmm3
    136         addsd     %xmm6, %xmm0
    137         mulpd     %xmm5, %xmm4
    138         movsd     2152(%ebx), %xmm6
    139         mulpd     %xmm5, %xmm5
    140         addpd     %xmm2, %xmm4
    141         mulpd     %xmm5, %xmm3
    142         pshufd    $228, %xmm0, %xmm2
    143         addsd     %xmm1, %xmm0
    144         mulsd     %xmm1, %xmm4
    145         subsd     %xmm0, %xmm2
    146         mulsd     %xmm1, %xmm6
    147         addsd     %xmm2, %xmm1
    148         pshufd    $238, %xmm0, %xmm2
    149         mulsd     %xmm5, %xmm5
    150         addsd     %xmm2, %xmm7
    151         addsd     %xmm6, %xmm1
    152         addpd     %xmm3, %xmm4
    153         addsd     %xmm7, %xmm1
    154         mulpd     %xmm5, %xmm4
    155         addsd     %xmm4, %xmm1
    156         pshufd    $238, %xmm4, %xmm5
    157         addsd     %xmm5, %xmm1
    158         addsd     %xmm1, %xmm0
    159         jmp       .L_2TAG_PACKET_2.0.2
    160 .L_2TAG_PACKET_0.0.2:
    161         movsd     112(%esp), %xmm0
    162         movapd    %xmm0, %xmm1
    163         addl      $16, %eax
    164         cmpl      $32768, %eax
    165         jae       .L_2TAG_PACKET_3.0.2
    166         cmpl      $16, %eax
    167         jb        .L_2TAG_PACKET_4.0.2
    168 .L_2TAG_PACKET_5.0.2:
    169         addsd     %xmm0, %xmm0
    170         jmp       .L_2TAG_PACKET_2.0.2
    171 .L_2TAG_PACKET_6.0.2:
    172         ja        .L_2TAG_PACKET_5.0.2
    173         cmpl      $0, %edx
    174         ja        .L_2TAG_PACKET_5.0.2
    175         jmp       .L_2TAG_PACKET_7.0.2
    176 .L_2TAG_PACKET_3.0.2:
    177         movd      %xmm1, %edx
    178         psrlq     $32, %xmm1
    179         movd      %xmm1, %ecx
    180         addl      %ecx, %ecx
    181         cmpl      $-2097152, %ecx
    182         jae       .L_2TAG_PACKET_6.0.2
    183         orl       %ecx, %edx
    184         cmpl      $0, %edx
    185         je        .L_2TAG_PACKET_8.0.2
    186 .L_2TAG_PACKET_7.0.2:
    187         xorpd     %xmm1, %xmm1
    188         xorpd     %xmm0, %xmm0
    189         movl      $32752, %eax
    190         pinsrw    $3, %eax, %xmm1
    191         movl      $9, %edx
    192         mulsd     %xmm1, %xmm0
    193 .L_2TAG_PACKET_9.0.2:
    194         movsd     %xmm0, (%esp)
    195         movsd     112(%esp), %xmm0
    196         fldl      (%esp)
    197         jmp       .L_2TAG_PACKET_10.0.2
    198 .L_2TAG_PACKET_8.0.2:
    199         xorpd     %xmm1, %xmm1
    200         xorpd     %xmm0, %xmm0
    201         movl      $49136, %eax
    202         pinsrw    $3, %eax, %xmm0
    203         divsd     %xmm1, %xmm0
    204         movl      $8, %edx
    205         jmp       .L_2TAG_PACKET_9.0.2
    206 .L_2TAG_PACKET_4.0.2:
    207         movd      %xmm1, %edx
    208         psrlq     $32, %xmm1
    209         movd      %xmm1, %ecx
    210         orl       %ecx, %edx
    211         cmpl      $0, %edx
    212         je        .L_2TAG_PACKET_8.0.2
    213         xorpd     %xmm1, %xmm1
    214         movl      $18416, %eax
    215         pinsrw    $3, %eax, %xmm1
    216         mulsd     %xmm1, %xmm0
    217         xorpd     %xmm2, %xmm2
    218         movl      $16368, %eax
    219         pinsrw    $3, %eax, %xmm2
    220         movapd    %xmm0, %xmm1
    221         pextrw    $3, %xmm0, %eax
    222         orpd      %xmm2, %xmm0
    223         movl      $18416, %ecx
    224         psllq     $5, %xmm0
    225         movsd     2144(%ebx), %xmm2
    226         psrlq     $34, %xmm0
    227         rcpss     %xmm0, %xmm0
    228         psllq     $12, %xmm1
    229         pshufd    $78, %xmm5, %xmm6
    230         psrlq     $12, %xmm1
    231         jmp       .L_2TAG_PACKET_1.0.2
    232 .L_2TAG_PACKET_2.0.2:
    233         movsd     %xmm0, 24(%esp)
    234         fldl      24(%esp)
    235 .L_2TAG_PACKET_10.0.2:
    236         movl      40(%esp), %ebx
    237         movl      %ebp, %esp
    238         popl      %ebp
    239         ret
    240 ..B2.3:
    241 END(log10)
    242 # -- End  log10
    243 
    244 # Start file scope ASM
    245 ALIAS_SYMBOL(log10l, log10);
    246 # End file scope ASM
    247 	.section .rodata, "a"
    248 	.align 16
    249 	.align 16
    250 static_const_table:
    251 	.long	1352628224
    252 	.long	1070810131
    253 	.long	521319256
    254 	.long	1025503025
    255 	.long	2150839296
    256 	.long	1070801944
    257 	.long	3329350096
    258 	.long	3170190015
    259 	.long	1360613376
    260 	.long	1070793794
    261 	.long	2024059075
    262 	.long	1024991594
    263 	.long	1875350528
    264 	.long	1070785680
    265 	.long	2163882141
    266 	.long	3163564137
    267 	.long	2312126464
    268 	.long	1070777602
    269 	.long	1975711076
    270 	.long	1023674196
    271 	.long	1306336256
    272 	.long	1070769560
    273 	.long	3524899523
    274 	.long	3170508164
    275 	.long	1806334976
    276 	.long	1070761553
    277 	.long	4254777025
    278 	.long	1025238739
    279 	.long	2483193856
    280 	.long	1070753581
    281 	.long	3800671317
    282 	.long	3172916830
    283 	.long	2025350144
    284 	.long	1070745644
    285 	.long	1731514745
    286 	.long	1025501083
    287 	.long	3433285632
    288 	.long	1070737741
    289 	.long	2551857336
    290 	.long	3169662186
    291 	.long	1134317568
    292 	.long	1070729873
    293 	.long	3426297655
    294 	.long	3172637891
    295 	.long	2457152512
    296 	.long	1070722038
    297 	.long	63549415
    298 	.long	1025415416
    299 	.long	1861803008
    300 	.long	1070714237
    301 	.long	1910171636
    302 	.long	1023977580
    303 	.long	2414140416
    304 	.long	1070706469
    305 	.long	4002514337
    306 	.long	3170841618
    307 	.long	2900726784
    308 	.long	1070698734
    309 	.long	3268064083
    310 	.long	1022459609
    311 	.long	2123517952
    312 	.long	1070691032
    313 	.long	1767031218
    314 	.long	1022448156
    315 	.long	3194569728
    316 	.long	1070683362
    317 	.long	3402332618
    318 	.long	3171671160
    319 	.long	650882048
    320 	.long	1070675725
    321 	.long	4146023905
    322 	.long	3171023038
    323 	.long	1928988672
    324 	.long	1070668119
    325 	.long	1438617867
    326 	.long	1016360491
    327 	.long	1594908672
    328 	.long	1070660545
    329 	.long	971389377
    330 	.long	1024763979
    331 	.long	2818746368
    332 	.long	1070653002
    333 	.long	3555925341
    334 	.long	3172434821
    335 	.long	194584576
    336 	.long	1070645491
    337 	.long	943919215
    338 	.long	3172950063
    339 	.long	1215096832
    340 	.long	1070638010
    341 	.long	2283358588
    342 	.long	1022335098
    343 	.long	501519360
    344 	.long	1070630560
    345 	.long	480904295
    346 	.long	1024437959
    347 	.long	1278266368
    348 	.long	1070623140
    349 	.long	2755806066
    350 	.long	3172342012
    351 	.long	2487812096
    352 	.long	1070615750
    353 	.long	2489653202
    354 	.long	3172481099
    355 	.long	3085451264
    356 	.long	1070608390
    357 	.long	3759184951
    358 	.long	3172574892
    359 	.long	2039090176
    360 	.long	1070601060
    361 	.long	1361176676
    362 	.long	3172355319
    363 	.long	953057280
    364 	.long	1070591423
    365 	.long	1176587546
    366 	.long	3166422018
    367 	.long	3370524672
    368 	.long	1070576879
    369 	.long	3669570051
    370 	.long	1025376630
    371 	.long	749742080
    372 	.long	1070562394
    373 	.long	707700964
    374 	.long	3170814058
    375 	.long	4008353792
    376 	.long	1070547965
    377 	.long	3247327652
    378 	.long	1022431400
    379 	.long	2612455424
    380 	.long	1070533594
    381 	.long	2453457344
    382 	.long	3172322969
    383 	.long	3230920704
    384 	.long	1070519279
    385 	.long	1296781801
    386 	.long	1025115335
    387 	.long	3965253632
    388 	.long	1070505020
    389 	.long	373075289
    390 	.long	1017938528
    391 	.long	2593157120
    392 	.long	1070476669
    393 	.long	1068054086
    394 	.long	1021616576
    395 	.long	925962240
    396 	.long	1070448537
    397 	.long	850121213
    398 	.long	1023928989
    399 	.long	1732556800
    400 	.long	1070420620
    401 	.long	1305206740
    402 	.long	3172665570
    403 	.long	3815630848
    404 	.long	1070392915
    405 	.long	192642943
    406 	.long	3172699907
    407 	.long	2001758208
    408 	.long	1070365420
    409 	.long	2820786683
    410 	.long	1024704867
    411 	.long	16746496
    412 	.long	1070338131
    413 	.long	1399573110
    414 	.long	3171372773
    415 	.long	1886492672
    416 	.long	1070311044
    417 	.long	3621428075
    418 	.long	3172974358
    419 	.long	3338196992
    420 	.long	1070284157
    421 	.long	3793882035
    422 	.long	1025124701
    423 	.long	381769728
    424 	.long	1070257468
    425 	.long	3877933342
    426 	.long	3170195490
    427 	.long	2186491904
    428 	.long	1070230972
    429 	.long	1838687089
    430 	.long	1017927292
    431 	.long	1008330752
    432 	.long	1070204668
    433 	.long	2228321664
    434 	.long	1025352196
    435 	.long	2247065600
    436 	.long	1070178552
    437 	.long	1413900906
    438 	.long	3170902532
    439 	.long	2964070400
    440 	.long	1070152622
    441 	.long	3590454629
    442 	.long	1025016844
    443 	.long	465154048
    444 	.long	1070126876
    445 	.long	2079688550
    446 	.long	3172268183
    447 	.long	883615744
    448 	.long	1070101310
    449 	.long	989244452
    450 	.long	3171900485
    451 	.long	1993768960
    452 	.long	1070075922
    453 	.long	1124327841
    454 	.long	3172964992
    455 	.long	1794471936
    456 	.long	1070050710
    457 	.long	1140575046
    458 	.long	1022673726
    459 	.long	2797932544
    460 	.long	1070025671
    461 	.long	1894836933
    462 	.long	3172544059
    463 	.long	3433797632
    464 	.long	1070000803
    465 	.long	3221831166
    466 	.long	3171921685
    467 	.long	2338371584
    468 	.long	1069976104
    469 	.long	3732461053
    470 	.long	3164513518
    471 	.long	2644013056
    472 	.long	1069951571
    473 	.long	2519460462
    474 	.long	3172548740
    475 	.long	3383814144
    476 	.long	1069927202
    477 	.long	2290997657
    478 	.long	1025499649
    479 	.long	3781380096
    480 	.long	1069902995
    481 	.long	380479405
    482 	.long	1025184136
    483 	.long	3245785088
    484 	.long	1069878948
    485 	.long	1096398261
    486 	.long	3169885192
    487 	.long	1366712320
    488 	.long	1069855059
    489 	.long	2218343715
    490 	.long	3170281628
    491 	.long	2204717056
    492 	.long	1069831325
    493 	.long	2668334011
    494 	.long	1025264524
    495 	.long	1401772032
    496 	.long	1069807745
    497 	.long	4103993159
    498 	.long	1022925721
    499 	.long	3356721152
    500 	.long	1069784316
    501 	.long	3573790772
    502 	.long	3172186527
    503 	.long	4041148416
    504 	.long	1069761037
    505 	.long	4027691910
    506 	.long	3171276990
    507 	.long	3880151040
    508 	.long	1069737906
    509 	.long	4087118786
    510 	.long	3172710734
    511 	.long	3453364224
    512 	.long	1069714921
    513 	.long	99014299
    514 	.long	3172003077
    515 	.long	3491092480
    516 	.long	1069692080
    517 	.long	3801836701
    518 	.long	3172989287
    519 	.long	575580160
    520 	.long	1069669382
    521 	.long	1920406012
    522 	.long	3170874125
    523 	.long	22282240
    524 	.long	1069646824
    525 	.long	964193370
    526 	.long	1019363159
    527 	.long	2991429632
    528 	.long	1069624404
    529 	.long	3372589890
    530 	.long	1023425053
    531 	.long	2189645824
    532 	.long	1069602122
    533 	.long	2610503872
    534 	.long	1023652442
    535 	.long	3341467648
    536 	.long	1069579975
    537 	.long	1190292004
    538 	.long	1022425665
    539 	.long	3711293440
    540 	.long	1069557962
    541 	.long	1104795356
    542 	.long	1023625829
    543 	.long	1380401152
    544 	.long	1069524644
    545 	.long	1156998217
    546 	.long	1025100499
    547 	.long	765710336
    548 	.long	1069481144
    549 	.long	1736649113
    550 	.long	1024999439
    551 	.long	849412096
    552 	.long	1069437902
    553 	.long	2618178330
    554 	.long	3170853629
    555 	.long	1433104384
    556 	.long	1069394915
    557 	.long	43477267
    558 	.long	3170378811
    559 	.long	2548596736
    560 	.long	1069352180
    561 	.long	3967367063
    562 	.long	1025246584
    563 	.long	157577216
    564 	.long	1069309695
    565 	.long	100402533
    566 	.long	3172825502
    567 	.long	3326238720
    568 	.long	1069267455
    569 	.long	1176892909
    570 	.long	1025464099
    571 	.long	4155494400
    572 	.long	1069225459
    573 	.long	3713707617
    574 	.long	3172630046
    575 	.long	3545804800
    576 	.long	1069183704
    577 	.long	857007315
    578 	.long	1024965777
    579 	.long	2602520576
    580 	.long	1069142187
    581 	.long	2588758347
    582 	.long	1022463131
    583 	.long	2631196672
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    791 	.type	static_const_table,@object
    792 	.size	static_const_table,2160
    793 	.data
    794 	.section .note.GNU-stack, ""
    795 # End
    796